Basis atomic orbital Slater type

In honour of J. C. Slater, we refer to such basis functions as Slater-type orbitals (STOs). Slater orbital exponents ( = (Z — s)/n ) for atoms through neon are given in Table 9.2. 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

Basis Functions. Functions usually centered on atoms which are linearly combined to make up the set of Molecular Orbitals. Except for Semi-Empirical Models where basis functions are Slater type, basis functions are Gaussian type. 

The entries in the first columns of the two tables are total energies of atoms given by the SCF calculations with the minimal basis set of Slater-type orbitals (STO, see Section 2.B.). The entries in the second columns are energies given by the calculations in which each STO was replaced by two Slater-type functions with the exponents so optimized to give the minimum total energy. From Tables 2.1 and... 

In brief, the CNDO (the acronym stands for complete neglect of differential overlap) approach is an all valence electron, self-consistent field calculation in which multicenter integrals have been neglected and some of the two electron integrals parameterized using atomic data. Slater type atomic orbitals are used as the basis 2s, 2px, 2p, 2p for carbon and oxygen. In these calculations two-electron in egrafs are approximated as... 

The standard extended Huckel Hamiltonian (23) with a minimum basis set of Slater-type atomic orbitals were used in all calculations. The overlap and Hamiltonian matrices were computed for the RC fragment in the light conformation (12), which included Bph Qa Qb, the iron ion and the relevant protein environment Met , Met , His ,... 

Minimal basis functions (e.g. STO-LG) contain only minimal required contracted functions for each atom. For example, since electrons occupy atomic orbitals up to the 2p orbital in the carbon atom, five contracted Gaussian-type functions corresponding to Is, 2s, 2p, 2py, and 2p orbitals are necessary at the minimum. The minimal basis functions approximating Slater-type orbitals (STO) corresponding to atomic orbitals with L prinoitive functions are called STO-LG basis functions. 

Kim has formulated a relativistic Hartree-Fock-Roothaan equation for the ground states of closed-shell atoms using Slater-type orbitals. Relativistic effects in atoms have been reviewed by Grant. Malli and coworkers have formulated a relativistic SCF method for molecules. In this method, four-component spinor wavefunctions are obtained variationally in a self-consistent scheme using Gaussian basis sets. 

Basis function-functions describing the atomic orbitals that when linearly combined make up the set of molecular orbitals in a quantum mechanics calculation Gaussian basis sets and Slater type orbitals are examples of basis functions. 

We seek a wave function that is a product of LCAOMOs. Table 21.1 shows the first three optimized LCAOMOs from a Hartree-Fock-Roothaan calculation using a minimal basis set of Slater-type orbitals Is, 2s, and 2on the Be atom and the two 1 s orbitals on the hydrogens. The six basis functions give six independent LCAOMOs, but... 

At the semiempirical level, explicit treatment is given to valence shell electrons only, and a minimal basis set of Slater-type s and p orbitals is assigned to each atom. The combined set of atomic basis functions (xi. Xz. . Ywl S used to... 

For both types of orbitals, the coordinates r, 0, and (j) refer to the position of the electron relative to a set of axes attached to the center on which the basis orbital is located. Although Slater-type orbitals (STOs) are preferred on fundamental grounds (e.g., as demonstrated in Appendices A and B, the hydrogen atom orbitals are of this form and the exact solution of the many-electron Schrodinger equation can be shown to be of this form (in each of its coordinates) near the nuclear centers), STOs are used primarily for atomic and linear-molecule calculations because the multi-center integrals < XaXbl g I XcXd > (each... 

These atomic orbitals, called Slater Type Orbitals (STOs), are a simplification of exact solutions of the Schrodinger equation for the hydrogen atom (or any one-electron atom, such as Li" ). Hyper-Chem uses Slater atomic orbitals to construct semi-empirical molecular orbitals. The complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and are not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

Minimal basis sets use fixed-size atomic-type orbitals. The STO-3G basis set is a minimal basis set (although it is not the smallest possible basis set). It uses three gaussian primitives per basis function, which accounts for the 3G in its name. STO stands for Slater-type orbitals, and the STO-3G basis set approximates Slater orbitals with gaussian functions. ... 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

There are two types of basis functions (also called Atomic Orbitals, AO, although in general they are not solutions to an atomic Schrodinger equation) commonly used in electronic structure calculations Slater Type Orbitals (STO) and Gaussian Type Orbitals (GTO). Slater type orbitals have die functional form... 

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